

from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np





class 					__lowerCAmelCase	(   __lowercase				):




  def     A__	(							self				,  lowerCAmelCase   )    ->					float:
        '''simple docstring'''






        return 0.0
def 	a (     A__      :  np.ndarray ,  A__      :  int	)       -> tuple[int | float, int | float]:





      """simple docstring"""



      _lowercase      			=min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
      _lowercase      			=max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
      return lowest, highest
def 	a (     A__      :  FilterType ,  A__      :  int	)       -> None:





      """simple docstring"""



      _lowercase      			=512
      _lowercase      			=[1] + [0] * (size - 1)
      _lowercase      			=[filter_type.process(_lowerCamelCase	) for item in inputs]

      _lowercase      			=[0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowercase      			=np.abs(np.fft.fft(_lowerCamelCase	)	)
      _lowercase      			=20 * np.logaa(_lowerCamelCase	)

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(24 ,  samplerate / 2 - 1	)
      plt.xlabel('Frequency (Hz)'	)
      plt.xscale('log'	)

      # Display within reasonable bounds
      _lowercase      			=get_bounds(_lowerCamelCase ,  _lowerCamelCase	)
      plt.ylim(max([-80, bounds[0]]	) ,  min([80, bounds[1]]	)	)
      plt.ylabel('Gain (dB)'	)

      plt.plot(_lowerCamelCase	)
      plt.show()







def 	a (     A__      :  FilterType ,  A__      :  int	)       -> None:





      """simple docstring"""



      _lowercase      			=512
      _lowercase      			=[1] + [0] * (size - 1)
      _lowercase      			=[filter_type.process(_lowerCamelCase	) for item in inputs]

      _lowercase      			=[0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowercase      			=np.angle(np.fft.fft(_lowerCamelCase	)	)

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(24 ,  samplerate / 2 - 1	)
      plt.xlabel('Frequency (Hz)'	)
      plt.xscale('log'	)

      plt.ylim(-2 * pi ,  2 * pi	)
      plt.ylabel('Phase shift (Radians)'	)
      plt.plot(np.unwrap(_lowerCamelCase ,  -2 * pi	)	)
      plt.show()




def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     int = 10**9)   ->       int:






							'''simple docstring'''





							__UpperCamelCase      :  int       =   1
							__UpperCamelCase      :  Any       =   2

							__UpperCamelCase      :  Dict       =   0
							__UpperCamelCase      :  Any       =   0
							__UpperCamelCase      :  List[Any]       =   0
							while perimeter <= max_perimeter:
														perimeters_sum += perimeter

														prev_value += 2 * value
														value += prev_value

														__UpperCamelCase      :  Optional[int]       =   2 * value + 2 if i % 2 == 0 else 2 * value - 2
														i += 1

							return perimeters_sum


if __name__ == "__main__":
		print(f"{solution() = }")